The title of the question already says it all but I would like to add that I would really like the book to be more about geometric algebra than its applications : it should contain theorems’ proofs. Just adding that I have never taken a course on geometric algebra. I’m a 2nd year engineering student, so a “beginner” book style will be very good!!! Also mentioning what would be the prerequisites for mastering the branch is appreciated. Thanks.
The classic reference is David Hestenes’ New Foundations for Classical Mechanics which is by one of the early developers of geometric algebra.
You may find it easier to learn geometric algebra from Geometric Algebra for Physicists by Doran and Lasenby though (I certainly did). The link is to a sample version of chapter 1.
A reference that I’ve never looked at is Geometric Algebra for Computer Science which details the geometric algebra approach to computer graphics, robotics and computer vision.
As for prerequisites – certainly some familiarity with linear algebra. For the ‘geometric calculus’ component a first course in multivariable calculus would be sufficient. Since the big developments in geometric algebra in the 1980s were by physicists, many of the examples tend to be physically motivated (spacetime algebras, relativistic electrodynamics etc) and a passing familiarity with (special) relativity, rigid body dynamics and electromagnetism would be useful (though certainly not essential).